Problem: Express this product in scientific notation: $(1.70\times 10^{-3})\times (6.00\times 10^{5})$
Answer: Start by collecting like terms together. $= (1.70\times 6.00) \times (10^{-3}\times 10^{5})$ When multiplying exponents with the same base, add the powers together. $= 10.2 \times 10^{-3\,+\,5}$ $= 10.2 \times 10^{2}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $10.2$ is the same as $1.020 \times 10$ $ = {1.020 \times 10} \times 10^{2} $ $= 1.020\times 10^{3}$